Logical Reasoning Improvement Dataset
Enhancing LLM Logical Reasoning Skills with Platypus2 Models
@kaggle.thedevastator_logical_reasoning_improvement_dataset
Train
@kaggle.thedevastator_logical_reasoning_improvement_dataset.train
- 14.62 MB
- 24926 rows
- 4 columns
inputInput | outputOutput | instructionInstruction | data_sourceData Source |
|---|---|---|---|
| nan | To find the probability of the spinner landing on $C$, I need to subtract the probabilities of the spinner landing on $A$ and $B$ from $1$, since the sum of the probabilities of all possible outcomes is $1$. I can write this as an equation: $P(C) = 1 - P(A) - P(B)$. I know that $P(A) = \frac{1}{3}$ … | A board game spinner is divided into three parts labeled $A$, $B$ and $C$. The probability of the spinner landing on $A$ is $\frac{1}{3}$ and the probability of the spinner landing on $B$ is $\frac{5}{12}$. What is the probability of the spinner landing on $C$? Express your answer as a common frac… | MATH/PRM-800K |
| nan | I need to choose 6 people out of 14, and the order does not matter. This is a combination problem, not a permutation problem. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of choices and r is the number of selections. Plugging in the numbers, I get 14C6 = 14! … | My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want 6 people on the team. In how many ways can I select the team without restrictions? | MATH/PRM-800K |
| nan | First we count the number of all 4-letter words with no restrictions on the word. Then we count the number of 4-letter words with no consonants. We then subtract to get the answer. Each letter of a word must be one of $A$, $B$, $C$, $D$, or $E$, so the number of 4-letter words with no restrictions … | How many 4-letter words with at least one consonant can be constructed from the letters $A$, $B$, $C$, $D$, and $E$? (Note that $B$, $C$, and $D$ are consonants, any word is valid, not just English language words, and letters may be used more than once.) | MATH/PRM-800K |
| nan | She can do this if and only if at least one of the dice lands on a 1. The probability neither of the dice is a 1 is $\left(\frac{5}{6}\right) \left(\frac{5}{6}\right) = \frac{25}{36}$. So the probability at least one die is a 1 is $1-\frac{25}{36} = \frac{11}{36}$. | Melinda will roll two standard six-sided dice and make a two-digit number with the two numbers she rolls. For example, if she rolls a 6 and a 3, she can either form 36 or 63. What is the probability that she will be able to make an integer between 10 and 20, inclusive? Express your answer as a commo… | MATH/PRM-800K |
| nan | Think of the problem as a sequence of H's and T's. No two T's can occur in a row, so the sequence is blocks of $1$ to $4$ H's separated by T's and ending in $5$ H's. Since the first letter could be T or the sequence could start with a block of H's, the total probability is that $3/2$ of it has to st… | Let $p$ be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of $5$ heads before one encounters a run of $2$ tails. Given that $p$ can be written in the form $m/n$ where $m$ and $n$ are relatively prime positive integers, find $m+n$. | MATH/PRM-800K |
| nan | For the first digit, there are seven choices (3, 4, 5, 6, 7, 8, or 9). For the last digit, there are ten choices (0 through 9). We know that if either of the middle digits is 0, their product will not exceed 5. So, only consider pairs of middle digits formed from choosing two numbers between 1 and … | How many four-digit numbers greater than 2999 can be formed such that the product of the middle two digits exceeds 5? | MATH/PRM-800K |
| nan | I need to find the average of all possible sums of two different marbles from the bag. To do that, I can list all the possible outcomes and their probabilities, and then multiply each outcome by its probability and add them up. There are 5 choose 2, or 10, ways to take out two different marbles from… | I have 5 marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles? | MATH/PRM-800K |
| nan | There are $\binom{11}{2} = 55$ combinations of two balls that can be drawn. There are $\binom{5}{2} = 10$ combinations of two white balls that can be drawn. So the probability that two balls pulled out are both white is $\dfrac{10}{55} = \dfrac{2}{11}$. | A box contains 5 white balls and 6 black balls. Two balls are drawn out of the box at random. What is the probability that they both are white? | MATH/PRM-800K |
| nan | The numbers $a_i - i$ are ten not-necessarily distinct even elements of the set $\{0, 1, 2, \ldots, 1997\}$. Moreover, given ten not-necessarily distinct elements of $\{0, 1, 2, \ldots, 1997\}$, we can reconstruct the list $a_1, a_2, \ldots, a_{10}$ in exactly one way, by adding 1 to the smallest, t… | The number of increasing sequences of positive integers $a_1 \le a_2 \le a_3 \le \cdots \le a_{10} \le 2007$ such that $a_i-i$ is even for $1\le i \le 10$ can be expressed as ${m \choose n}$ for some positive integers $m > n$. Compute the remainder when $m$ is divided by 1000. | MATH/PRM-800K |
| nan | There are $\left\lfloor\frac{999}{10}\right\rfloor = 99$ numbers up to 1000 that have 0 as their units digit. All of the other excluded possibilities are when $a$ or $b$ have a 0 in the tens digit, and since the equation is symmetric, we will just count when $a$ has a 0 in the tens digit and multipl… | Find the number of ordered pairs of positive integers $(a,b)$ such that $a+b=1000$ and neither $a$ nor $b$ has a zero digit. | MATH/PRM-800K |
CREATE TABLE train (
"input" VARCHAR,
"output" VARCHAR,
"instruction" VARCHAR,
"data_source" VARCHAR
);